Topology in quantum mechanics. In 1959 Aharonov and Bohm [1]} considered charged particles excluded by an infinite potential barrier from a cylindrical region, behind which a current in a tightly-wound infinitely-long solenoid sustains a magnetic flux. Quantum theory then predicts shifts in the energy and kinetic angular momentum spectrum of the particles, despite the absence of a physical magnetic field in the accessible region. Their paper, conceived as a Gedanken experiment, evoked much controversy as to its meaning. Though known as the “Aharonov-Bohm effect”, a similar but much less noticed proposal had actually been published in 1949 by Ehrenberg and Siday [2]}, as Hiley describes in a historical article [3]}. The earlier work is highlighted in the Wikipedia entry on the subject [4]}, which is how I learned of it just last year. The (Ehhrenberg-Siday)-Aharonov-Bohm effect pointed to the role of the topology of the space in which quantum particles move – particularly, but not exclusively, when charged particles circle excluded regions of magnetic flux. The possibility of multivalued wave functions needed to be entertained – though challenged, it began to achieve legitimacy.
